Rolling bearings are known to comprise at least two components, specifically an inner race and an outer race, between which the rolling bodies, be they balls or rollers or the like, run. Rotationally symmetrical rolling bearing components of this type are conventionally produced in material-removing fashion and are subsequently case-hardened or carbonitrided in order to improve the rolling fatigue strength. Owing to the stresses which occur, high carburizing depths of more than 2 mm are required, for example, during case-hardening and these cause the duration of the heat treatment to be at least 15-20 hours, depending on the selected material. Further modifications of the surface layer properties are possible only by selecting a different base material which is generally more highly alloyed. The change to a higher-grade base material is, however, associated with greater costs.